Question: A standard die is rolled six times. What is the probability that the product of all six rolls is odd? Express your answer as a common fraction.
Solution: The product of all six rolls is odd if and only if each roll is odd.  Any given roll has an odd result with probability $\frac{1}{2}$.  The probability of all six rolls being odd is therefore $\left(\frac{1}{2}\right)^6 = \boxed{\frac{1}{64}}$.